robust: Robustification and Hermite Interpolation for ICMA

Description Usage Arguments Value Note Author(s) References

Description

Performs robustification and Hermite interpolation in the iterative convex minorant algorithm as described in Rufibach (2006, 2007).

Usage

1
robust(x, w, eta, etanew, grad)

Arguments

x

Vector of independent and identically distributed numbers, with strictly increasing entries.

w

Optional vector of nonnegative weights corresponding to x_m.

eta

Current candidate vector.

etanew

New candidate vector.

grad

Gradient of L at current candidate vector η.

Value

Returns a (possibly) new vector η on the segment

(1 - t_0) η + t_0 η_{new}

such that the log-likelihood of this new η is strictly greater than that of the initial η and t_0 is chosen according to the Hermite interpolation procedure described in Rufibach (2006, 2007).

Note

This function is not intended to be invoked by the end user.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

References

Rufibach K. (2006) Log-concave Density Estimation and Bump Hunting for i.i.d. Observations. PhD Thesis, University of Bern, Switzerland and Georg-August University of Goettingen, Germany, 2006.
Available at http://www.zb.unibe.ch/download/eldiss/06rufibach_k.pdf.

Rufibach, K. (2007) Computing maximum likelihood estimators of a log-concave density function. J. Stat. Comput. Simul. 77, 561–574.


logcondens documentation built on May 2, 2019, 6:11 a.m.